Question

answer pls i will mark brainliest

Answer 1

Question:

• The radius and the height of a cone are in the ratio 7:3. If the volume of a cone is 9856cm³ then the height of the cone is

Answer:

Given:

• $\large{\bf{ \: \: \: \: \: \: \: \: \:\bigg\{^{Ratio~of~radius~to~height = 7:3}_{Volume~of~cone~=~9856cm³}}}$

To Find:

• $\small{\bf{\longmapsto{Height~of~cone?}}}$

Solution:

As per given question, we know that Radius : Height of cone is 7:3.

Let suppose that common of ratio is x

Therefore,

• Height of cone = 3x
• Radius of cone = 7x

We know that :

• $\small{\tt{Volume~of~cone~=~\dfrac{πr²h}{3}}}$

Put given values in formula :

$\small{\tt{Volume~of~cone~=~\dfrac{πr²h}{3}}}$

$\implies\small{\tt{9856~=~\dfrac{22×(7x)²×3x}{7×3}}}$

$\implies\small{\tt{9856~=~\dfrac{22×49x²×3x}{21}}}$

$\implies\small{\tt{9856×\dfrac{21}{22}~=~49x²×3x}}$

$\implies\small{\tt{\cancel{9856}}×\dfrac{21}{\cancel{22}}~=~147x³}$

$\implies\small{\tt{448×21~=~147x³}}$

$\implies\small{\tt{9408~=~147x³}}$

$\implies\small{\tt{x³~=~\dfrac{9408}{147}}}$

$\implies\small{\tt{x³~=~64}}$

$\implies\small{\tt{x~=~\sqrt[3]{64}}}$

$\implies\small{\pink{\tt{x~=~4}}}$

Therefore,

• common of ratio is 4

Hence,

• $\large{\underline{\boxed{\bf{\red{Height~of~cone~=~3×4~→12cm}}}}}$